We show that, for any fixed δ > 0, the combinatorial complexity of the union of n triangles in the plane, each of whose angles is at least δ, is O(n2^α(n) log* n), with the constant of proportionality depending on δ. This considerably improves the twenty-...

In this talk, I will discuss some "textbook exercises" in low-dimensional computational geometry that any algorithmist with no computational-geometry background can attempt to solve: Given a set of red and blue points, is there a red point dominating (...

Multiple objects in the plane are called pseudodisks if they are convex and the boundaries of any two of them intersect transversely at most twice. Given a set of n (possibly intersecting) pseudodisks of O(1) complexity each and two points s and t in the ...

Let G be an n-vertex plane graph with non-negative edge weights, and let k terminal pairs be specified on h face boundaries. We present an algorithm to find k non-crossing walks in G of minimum total length that connect all terminal pairs, if any such ...